The document discusses the time value of money concept. It explains that money has a higher value today than in the future due to its ability to earn interest over time. There are two main techniques used to evaluate the time value of money: 1) compounding, which calculates the future value of an investment, and 2) discounting, which determines the present value of a future amount. An example is provided to illustrate compounding, showing how interest compounds annually on a Rs. 1,000 investment over three years. A second example demonstrates how to use discounting to calculate that the present value of Rs. 1,060 to be received one year in the future, with a 6% interest rate, is Rs. 1,000

1. TIME VALUE OF MONEY
•Rationale
•Technique
•Example

2. Time Value of Money
• Time value of money means that the value of a unit of
money is different in different time periods. Money has time
value. A rupee today is more valuable than a rupee a year
hence. A rupee a year hence has less value than a rupee
today. Money has, thus, a future value and a present value.
Although alternatives can be assessed by either
compounding to find future value or discounting to find
present value, financial managers rely primarily on present
value techniques as they are at zero time (t = 0) when
making decisions.
Techniques:
1.Computing Techniques
2.Discounting Techniques

3. Compounding Technique
• Interest is compounded when the amount
earned on an initial deposit (the initial
principal) becomes part of the principal at
the end of the first compounding period. The
term principal refers to the amount of money
on which interest is received. Consider
Example 1.

4. Example: Compounding Technique
• If Mr X invests in a saving bank account Rs 1,000
at 5 per cent interest compounded annually, at
the end of the first year, he will have Rs 1,050 in
his account. This amount constitutes the
principal for earning interest for the next year.
At the end of the next year, there would be Rs
1,102.50 in the account. This would represent
the principal for the third year. The amount of
interest earned would be Rs 55.125. The total
amount appearing in his account would be Rs
1,157.625. Table 1 shows this compounding
procedure:

5. Annual Compounding
Year 1 2 3
Beginning amount Rs 1,000.00 Rs 1,050.00 Rs 1,102.500
Interest rate 0.05 0.05 0.050
Amount of interest 50.00 52.50 55.125
Beginning principal 1,000.00 1,050.00 1,102.500
Ending Principal 1,050.00 1,102.50 1,157.625

6. This compounding procedure will continue for an indefinite number of
years. The compounding of interest can be calculated by the following
equation:
A = P (1 + i)n
(1)
A = amount at the end of the period
P = principal at the beginning of the period
i = rate of interest
n = number of years
The amount of money in the account at the end of various years is
calculated by using Eq. 1.
Amount at the end of year
1 = Rs 1,000 (1 + .05) = Rs 1,050
2 = Rs 1,050 (1 + .05) = Rs 1,102.50
3 = Rs 1,102.50 (1 + .05) = Rs 1,157.625
The amount at the end of year 2 can be ascertained by substituting Rs 1,000
(1 + .05) for Rs 1,050, that is, Rs 1,000 (1 + .05) (1 + .05) = Rs 1,102.50.
Similarly, the amount at the end of year 3 can be determined in the
following way: Rs 1,000 (1 + .05) (1 + .05) (1 + .05) = Rs 1,157.625.

7. Present Value or Discounting
Technique
• Present Value Present value is the current
value of a future amount . The amount to be
invested today at a given interest rate over a
specified period to equal the future amount
• Discounting is determining the present value
of a future amount.

8. Example: Present Value
Mr X has been given an opportunity to receive Rs 1,060 one year from now. He knows that he can
earn 6 per cent interest on his investments. The question is: what amount will he be prepared to
invest for this opportunity?
To answer this question, we must determine how many rupees must be invested at 6 per cent today
to have Rs 1,060 one year afterwards.
Let us assume that P is this unknown amount, and using Eq. 1 we have: P(1 + 0.06) = Rs 1,060
Solving the equation for P, P = (Rs 1,060 / 1.06) = Rs 1,000
Thus, Rs 1,000 would be the required investment to have Rs 1,060 after the expiry of one year. In
other words, the present value of Rs 1,060 received one year from now, given the rate of interest
of 6 per cent, is Rs 1,000. Mr X should be indifferent to whether he receives Rs 1,000 today or Rs
1,060 one year from today. If he can either receive more than Rs 1,060 by paying Rs 1,000 or Rs
1,060 by paying less than Rs 1,000, he would do so.
Mathematical Formulation
P= A /(1+i)n = A {1/(1+i)}n Eq. 2
in which P is the present value for the future sum to be received or spent; A is the sum to be received
or spent in future; i is interest rate, and n is the number of years. Thus, the present value of
money is the reciprocal of the compounding value.

9. Thank You

10. Thank You